ON THE COLEMAN-HILL THEOREM

The Coleman-Hill theorem prohibits the appearance of radiative correct ions to the topological mass (more precisely, to the parity-odd part o f the vacuum polarization tenser at zero momentum) in a wide class of abelian gauge theories in 2 + 1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum po larization tenser. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Si mons electrodynamics, obeys the new non-renormalization theorem. Where as the vacuum polarization does receive a one-loop, parity-odd correct ion, this does not translate to a radiative contribution to the Chem-S imons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooke d in the original analysis, where the conditions of the theorem are sa tisfied and where the topological mass does, in fact, get a radiative correction.